Which of the following numbers is a factor of 143? ${6,10,12,13,14}$
By definition, a factor of a number will divide evenly into that number. We can start by dividing $143$ by each of our answer choices. $143 \div 6 = 23\text{ R }5$ $143 \div 10 = 14\text{ R }3$ $143 \div 12 = 11\text{ R }11$ $143 \div 13 = 11$ $143 \div 14 = 10\text{ R }3$ The only answer choice that divides into $143$ with no remainder is $13$ $ 11$ $13$ $143$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $13$ are contained within the prime factors of $143$ $143 = 11\times13 13 = 13$ Therefore the only factor of $143$ out of our choices is $13$. We can say that $143$ is divisible by $13$.